An optical waveguide typically has a region of high refractive index surrounded by a region of low refractive index. The high-low refractive index profile provides the required light guiding effect as the optical radiation is reflected back to the high refractive index region at the interface of the two regions.
Optical waveguides presently find many applications in technology and will undoubtedly be even more widely used in the future. For example, optical waveguides are commonly used to guide light between two optical devices. The waveguide can be an optical fiber guiding light between a light source and a photodetector. Optical fibers typically have a high-index cylindrical core surrounded by a low-index clad. Waveguides are also used in many types of devices including electro-optic devices using LiNbO.sub.3 as well as semiconductor lasers. Waveguides may also be used to connect different optical devices.
For many applications, the waveguides must either be curved or have varying transverse dimensions, i.e., they are tapered. These characteristics are often required, e.g., to connect devices having different dimensions or to switch the optical signals from one waveguide to another waveguide. However, practical implementation of low-loss waveguides having these characteristics is not easy. For example, curved waveguides may have extremely high radiation losses unless very large radii of curvature are used. The currently used optical waveguides are formed by indiffusing Ti into LiNbO.sub.3, and they may be bent only very slightly to avoid prohibitively high radiation losses. A typical radius of curvature is about 2 cm at a wavelength of approximately 1.3 .mu.m. Such a relatively large radius of curvature is undesirable for several reasons. For example, optical circuits using such waveguides tend to be long and skinny thereby making an inefficient use of the crystal surface as only relatively thin strips are effectively utilized. Additionally, there are some devices such as, e.g., ring filters and ring lasers which require optical feedback and are not currently feasible because of the large radius of curvature required.
A simple physical argument may be used to show that the conventional curved dielectric waveguide should be lossy because of radiation. Assume that the waveguide is a curved slab having a constant thickness and curvature with a uniform refractive index inside the slab which is larger than the uniform refractive index outside the slab. The phase fronts of the radiation in the waveguide should move at the same speed, that is, the phase fronts should be rotating planes. It will be readily appreciated that the phase fronts have zero speed at zero radius and approach infinite velocity as the radius becomes large. However, since the velocity of the energy cannot exceed the speed of light, radiation from the waveguide must necessarily occur. Therefore, this curved waveguide is lossy.
Another type of problem also leading to losses often occurs when a waveguide is used to connect devices of different physical dimensions. This problem may arise, e.g., when the waveguide is used to connect a semiconductor laser to an optical fiber or one optical fiber to another when the the two have significantly different physical dimensions. The waveguide is typically tapered, i.e., it has a varying transverse dimension, so that the dimensions of the waveguide match those of the devices at the device-waveguide interfaces.
The fact that such a waveguide may be lossy is easily understood from the following physical argument. Assume that the waveguide is a linearly tapered slab with a uniform refractive index outside the slab and a larger and uniform refractive index inside the slab. If the electromagnetic radiation propagates from the wide end to the narrow end, a point is eventually reached at which the waveguide is sufficiently narrow so that at least one mode is no longer guided and radiates.
Attempts have been made to design waveguides having parameters chosen to minimize losses. See, for example, Applied Optics, 13, pp. 642-647, March 1974; Applied Optics, 16, pp. 711-716, March 1977; Applied Optics, 17, pp. 763-768, March 1978; IEEE Journal of Quantum Electronics, QE-11, pp. 75-83, February 1975; and IEEE Journal of Quantum Electronics, QE-18, pp. 1802-1806, October 1982.